English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We characterize optimal rank-1 matrix approximations with Hankel or Toeplitzstructure with regard to two different norms, the Frobenius norm and thespectral norm, in a new way. More precisely, we show that these rank-1 matrixapproximation problems can be solved by maximizing special rational functions.Our approach enables us to show that the optimal solutions with respect tothese two norms have completely different structure and only coincide in thetrivial case when the singular value decomposition already provides an optimalrank-1 approximation with the desired Hankel or Toeplitz structure.  We also prove that the Cadzow algorithm for structured low-rankapproximations always converges to a fixed point in the rank-1 case. However,it usually does not converge to the optimal solution, neither with regard tothe Frobenius norm nor the spectral norm.

Optimal Rank-1 Hankel Approximation of Matrices: Frobenius Norm, Spectral Norm, and Cadzow's Algorithm